{
  "id": "1408.4252",
  "version": "v1",
  "published": "2014-08-19T08:46:57.000Z",
  "updated": "2014-08-19T08:46:57.000Z",
  "title": "Diffeomorphisms with positive metric entropy",
  "authors": [
    "Artur Avila",
    "Sylvain Crovisier",
    "Amie Wilkinson"
  ],
  "comment": "77 pages, 13 figures",
  "categories": [
    "math.DS"
  ],
  "abstract": "We obtain a dichotomy for $C^1$-generic, volume preserving diffeomorphisms: either all the Lyapunov exponents of almost every point vanish or the volume is ergodic and non-uniformly Anosov (i.e. hyperbolic and the splitting into stable and unstable spaces is dominated). We take this dichotomy as a starting point to prove a $C^1$ version of a conjecture by Pugh and Shub: among partially hyperbolic volume-preserving $C^r$ diffeomorphisms, $r>1$, the stably ergodic ones are $C^1$-dense. To establish these results, we develop new perturbation tools for the $C^1$ topology: \"orbitwise\" removal of vanishing Lyapunov exponents, linearization of horseshoes while preserving entropy, and creation of \"superblenders\" from hyperbolic sets with large entropy.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-08-19T08:46:57.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37C05",
      "37C20",
      "37C40",
      "37D25",
      "37D30"
    ],
    "keywords": [
      "positive metric entropy",
      "hyperbolic sets",
      "volume preserving diffeomorphisms",
      "vanishing lyapunov exponents",
      "large entropy"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 77,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1408.4252A"
    }
  }
}